FERGUSON, Mo. — Missouri Gov. Jay Nixon said Tuesday that he would not seek the removal of the county prosecutor overseeing the investigation into the fatal police shooting of Michael Brown, which has sparked more than a week of nightly clashes between protesters and police.

St. Louis County Prosecutor Bob McCulloch’s deep family connections to police have been cited by some black leaders who question his ability to be impartial. McCullouch’s father, mother, brother, uncle and cousin all worked for the St. Louis Police Department, and his father was killed while responding to a call involving a black suspect.

Nixon said he would not ask McCulloch to leave the case, citing the “well-established process” by which prosecutors can recuse themselves from pending investigations to make way for a special prosecutor.

Departing from that process, Nixon said in a statement, “could unnecessarily inject legal uncertainty into this matter and potentially jeopardize the prosecution.”

McCulloch, a Democrat, was elected in 1991 and has earned a reputation for being tough on crime.

After sundown Tuesday, the streets of Ferguson filled once more with protesters, but the scene was much more subdued than recent nights, with somewhat smaller crowds. There were no immediate reports of clashes with police, who stood by with batons and gas masks.

Earlier in the day, Ferguson city leaders urged people to stay home after dark Tuesday to “allow peace to settle in” and pledged to try to improve the police force in the St. Louis suburb

In a public statement, the city said the mayor, the City Council and employees have been exploring ways to increase the number of African-American applicants to the law enforcement academy, develop incentive programs to encourage city residency for police officers and raise money for cameras that would be attached to patrol car dashboards and officers’ vests.

“We plan to learn from this tragedy, as we further provide for the safety of our residents and businesses and progress our community through reconciliation and healing,” the statement said.

Benjamin Crump, an attorney for Brown’s family, said the 18-year-old’s funeral and memorial service would be Monday. The time and location had not been finalized.

Earlier Tuesday, a large crowd gathered in nearby St. Louis after officers responding to a report of a store robbery shot and killed a knife-wielding man. Police Chief Sam Dotson said the suspect acted erratically and told responding officers to “kill me now.”

Some members of the crowd shouted, “Hands up, don’t shoot,” a phrase that has been a refrain of protests since Brown’s death on Aug. 9. Like Brown, the 23-year-old suspect killed Tuesday was black.

A grand jury could begin hearing evidence Wednesday to determine whether the officer, Darren Wilson, should be charged in Brown’s death, said Ed Magee, spokesman for St. Louis County’s prosecuting attorney.

Wilson was recognized during a Ferguson City Council meeting in February, getting special recognition for what Police Chief Thomas Jackson said then was his role in responding to a report of a suspicious vehicle, then struggling with the driver and detaining him until help arrived. Jackson said the suspect was preparing a large quantity of marijuana for sale.

Attorney General Eric Holder was scheduled to travel to Ferguson on Wednesday to meet with FBI and other officials carrying out an independent federal investigation into Brown’s death.

The Justice Department has mounted an unusually swift and aggressive response to Brown’s death, from the independent autopsy to dozens of FBI agents combing Ferguson for witnesses to the shooting.

The Justice Department arranged for a third autopsy to be performed by one of the military’s most experienced medical examiners, Holder said.

On Monday night, the National Guard arrived in Ferguson but kept its distance from the streets during another night of unrest.

Capt. Ron Johnson of the Missouri Highway Patrol, who is in charge of security in Ferguson, said bottles and Molotov cocktails were thrown from the crowd and that some officers came under heavy gunfire. Police originally said 31 were arrested, but St. Louis County spokeswoman Candace Jarrett on Tuesday said 57 people were booked at the county jail alone, and perhaps more at other jails in the region.

A list of those arrested showed that only four live in Ferguson, though many live in St. Louis and other surrounding communities. Sixteen are from out of state.